Automatic Blocking of Shapes Using Evolutionary Algorithm

This work focuses on the use of evolutionary algorithm to perform automatic blocking of a 2D manifold. The goal of such a blocking process is to completely partition a 2D region into a set of conforming and non-intersecting quadrilaterals to facilitate the generation of an all-quadrilateral, or more preferably an ideal quadrilateral mesh configuration covering the closed 2D region. However, depending on the input shape, the optimal blocking strategy is often unclear and can be very user-dependent. In this work, a novel approach based on evolutionary algorithm is adapted to search for a potential set of such ideal configurations. Based on a selection within a set of candidate vertices from a pre-computed pool, blocking configurations can be derived and ranked based on the collective quality of its blocks. The quality of a block is computed based on objective functions relating to its interior angles and opposite length ratios. Using multi-dimensional ranking criteria, inferior solutions can be slowly filtered away with each successive generation. Based on observations on a range of turbomachinery test cases, it is possible to derive and improve near-optimal blocking configurations by utilizing a large number of generations. This work has the potential to be extensible to 3D shapes as well.

[1]  C. Lee,et al.  A new scheme for the generation of a graded quadrilateral mesh , 1994 .

[2]  E. Catmull,et al.  Recursively generated B-spline surfaces on arbitrary topological meshes , 1978 .

[3]  John W. Morse,et al.  Prediction of halite, gypsum, and anhydrite solubility in natural brines under subsurface conditions , 1993 .

[4]  Guoqun Zhao,et al.  Automatic quadrilateral mesh generation and quality improvement techniques for an improved combination method , 2015, Computational Geosciences.

[5]  Jeff Erickson,et al.  Automatic Blocking Scheme for Structured Meshing in 2d Multiphase Flow Simulation , 2004, IMR.

[6]  Mohamed S. Ebeida,et al.  Guaranteed-Quality All-Quadrilateral Mesh Generation with Feature Preservation , 2009, IMR.

[7]  David R. White,et al.  Redesign of the Paving Algorithm : Robustness Enhancements through Element by Element Meshing , 2007 .

[8]  T. Tam,et al.  2D finite element mesh generation by medial axis subdivision , 1991 .

[9]  Steven J. Owen,et al.  A Survey of Unstructured Mesh Generation Technology , 1998, IMR.

[10]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[11]  Paul G. Tucker,et al.  Optimal mesh topology generation for CFD , 2017 .

[12]  Franck Ledoux,et al.  A PDE Based Approach to Multidomain Partitioning and Quadrilateral Meshing , 2012, IMR.

[13]  Keisuke Inoue,et al.  Automated Conversion of 2D Triangular Mesh into Quadrilateral Mesh with Directionality Control , 1998, IMR.

[14]  Kenji Shimada,et al.  An Angle-Based Approach to Two-Dimensional Mesh Smoothing , 2000, IMR.

[15]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[16]  Paul G. Tucker,et al.  Fast equal and biased distance fields for medial axis transform with meshing in mind , 2011 .

[17]  Shahrokh Shahpar,et al.  PADRAM: Parametric Design and Rapid Meshing System for Complex Turbomachinery Configurations , 2012 .

[18]  Dietrich Nowottny,et al.  Quadrilateral Mesh Generation via Geometrically Optimized Domain Decomposition , 1997 .

[19]  Matthew L. Staten,et al.  Advancing Front Quadrilateral Meshing Using Triangle Transformations , 1998, IMR.

[20]  Jeffrey A. Talbert,et al.  Development of an automatic, two‐dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition , 1990 .

[21]  F. Betul Atalay,et al.  Quadrilateral meshes with provable angle bounds , 2011, Engineering with Computers.

[22]  Christopher M. Tierney,et al.  Common Themes in Multi-block Structured Quad/Hex Mesh Generation , 2015 .

[23]  Yongjie Zhang,et al.  Adaptive and Quality Quadrilateral/Hexahedral Meshing from Volumetric Data. , 2006, Computer methods in applied mechanics and engineering.

[24]  Barry Joe,et al.  Quadrilateral mesh generation in polygonal regions , 1995, Comput. Aided Des..

[25]  Zaib Ali,et al.  Multiblock Structured Mesh Generation for Turbomachinery Flows , 2013, IMR.

[26]  Ted D. Blacker,et al.  Paving: A new approach to automated quadrilateral mesh generation , 1991 .

[27]  Jeanne Pellerin,et al.  Identifying combinations of tetrahedra into hexahedra: A vertex based strategy , 2017, Comput. Aided Des..

[28]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[29]  Harold J. Fogg,et al.  Multi_Block Decomposition Using Cross-Fields , 2013 .

[30]  Daniele Panozzo,et al.  Practical quad mesh simplification , 2010, Comput. Graph. Forum.

[31]  Harold J. Fogg,et al.  Automatic generation of multiblock decompositions of surfaces , 2015 .